In a lithography process for manufacturing electronic devices (micro-devices) such as a liquid crystal display device, a semiconductor device and the like, a projection exposure apparatus of a step-and-repeat method (a so-called stepper), a projection exposure apparatus of a step-and-scan method (a so-called scanning stepper (also called a scanner)), and the like are mainly used. As for exposure apparatuses for liquid crystal display devices (liquid crystal exposure apparatus), due to the increasing size of the substrates, a scanning type projection exposure apparatus such as the scanner is now mainstream.
Electronic devices (micro-devices) are manufactured by forming a plurality of layers of patterns that are overlaid on a substrate (a glass plate, a wafer and the like). Therefore, in the exposure apparatus, it is necessary to accurately overlay and transfer a pattern of a mask onto a pattern which is already formed in each shot area on the substrate, that is, high overlay accuracy is required.
To achieve the high overlay accuracy, a precise and stable control technique of a substrate stage which moves holding the substrate will be required. Here, in recent years, as the substrate stage, a gantry stage which is equipped with a carriage that moves in a scanning direction of the substrate at the time of scanning exposure and a substrate table that is supported on the carriage and moves in a non-scanning direction holding the substrate is mainly employed. In the gantry stage and the like, resonance occurs which becomes a failure cause to an accurate and stable control of the substrate stage. Especially recently, with size of the substrate stage increasing, the resonance frequency tends to be low.
As a theoretical framework to structure a control system using a notch filter, the control system being of a high frequency band including a resonance region of such substrate stages and also being robust to variation of resonant frequency, a stage controller is known that utilizes an advanced robust control theory represented by an H-infinity control theory (for example, refer to PTL 1). In the advanced robust control theory, while a sensor is added to make a plant a single-input multiple-output system, there are no restrictions to placement of the added sensor, and further, a feedback controller which is also stable to a modeling error of a nominal model can be designed. However, because degrees of freedom when designing a controller increases in general according to the plant structure, order of a weight function and the like, a trade-off relation occurs between high bandwidth and robustness of the feedback controller.